Most of the time, we propose models whose likelihoods and priors have an explicit closed-form probability densities. In some occasions, however, if we are able to sample from a simulator that is better at modeling the generative mechanism that gives rise to the data, then we can refrain from specifying an explicit probability density for either the data distribution or the prior. Models that do not specify explicit densities are known in the literature as implicit models, first introduced by [1]} to approximate an intractable likelihood and later extended to approximating the posterior distribution by [2]} in a method that is now known as Approximate Bayesian Computation (ABC) [3]}. In an implicit model, instead of defining a likelihood, we define a deterministic function \(f(.)\)  whose input is a random noise source \(\epsilon _n\)  and whose output is the observation
\(\mathbf {y}_n= f(\epsilon _n \mid \mathbf {z}_n, \theta ); \quad \epsilon _n \sim \ s(·)\) 
